Represent the following situations in the form of quadratic equations.
(i) The area of a rectangular plot is \(528\) m\(^2\). The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.
Required quadratic equation \(=\)
(ii) The product of two consecutive positive integers is \(306\). We need to find the integers.
Required quadratic equation \(=\)
(iii) Vihaan’s mother is \(26\) years older than him. The product of their ages (in years) \(3\) years from now will be \(360\). We would like to find Vihaan’s present age.
Required quadratic equation \(=\)
(iv) A train travels a distance of \(480 km\) at a uniform speed. If the speed had been \(8 km/h\) less, then it would have taken \(3\) hours more to cover the same distance. We need to find the speed of the train.
Required quadratic equation \(=\)
(v) John and Arav together have \(45\) marbles. Both of them lost \(5\) marbles each, and the product of the number of marbles they now have is \(124\). We would like to findout how many marbles they had to start with.
Required quadratic equation \(=\)
(vi) A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be \(55\) minus the number of toys produced in a day. On a particular day, the total cost of production was \(₹ 750\). We would like to find out the number of toys produced on that day.
Required quadratic equation \(=\)
Answer variants:
\(x^2-55x+750=0\)
\(x^2+32x-273=0\)
\(x^2-45x+324=0\)
\(2x^2+x-528=0\)
\(x^2+x-306=0\)
\(x^2-8x-1280=0\)